(From cond-mat/0503505): The conventional definition of spin current is incomplete and unphysical in describing spin transport in systems with spin-orbit coupling. A proper and measurable spin current is established in this study, which fits well into the standard framework of near-equilibrium transport theory and has the desirable property to vanish in insulators with localized orbitals. Our theory predicts opposite signs of spin Hall coefficients for a few semiconductor models, urging critical tests of the concept by experiments and numerics.